re shown by the dotted lines in a figure
titled "The 'pear-shaped figure' and the Jocobian figure from which it
is derived" (Fig. 3.) comprising two figures, one above the other: the
upper figure is the equatorial section at right angles to the axis of
rotation, the lower figure is a section through the axis.

Now Poincare has proved that the new type of figure is to be derived
from the figure of bifurcation by causing one of the ends to be
prolonged into a snout and by bluntening the other end. The snout forms
a sort of stalk, and between the stalk and the axis of rotation the
surface is somewhat flattened. These are the characteristics of a pear,
and the figure has therefore been called the "pear-shaped figure of
equilibrium." The firm line shows this new type of figure, whilst, as
already explained, the dotted line shows the form of bifurcation
from which it is derived. The specific mark of this new family is the
protrusion of the stalk together with the other corresponding smaller
differences. If we denote this difference by c, while A + b denotes the
Jacobian figure of bifurcation from which it is derived, the new family
may be called A + b + c, and c is zero initially. According to my
calculations this series of figures is stable (M. Liapounoff contends
that for constant density the new series of figures, which M. Poincare
discovered, has less rotational momentum than that of the figure of
bifurcation. If he is correct, the figure of bifurcation is a limit of
stable figures, and none can exist with stability for greater rotational
momentum. My own work seems to indicate that the opposite is true, and,
notwithstanding M. Liapounoff's deservedly great authority, I venture
to state the conclusions in accordance with my own work.), but I do not
know at what stage of its development it becomes unstable.

Professor Jeans has solved a problem which is of interest as throwing
light on the future development of the pear-shaped figure, although
it is of a still more ideal character than the one which has been
discussed. He imagines an INFINITELY long circular cylinder of liquid
to be in rotation about its central axis. The existence is virtually
postulated of a demon who is always occupied in keeping the axis of the
cylinder straight, so that Jeans has only to concern himself with the
stability of the form of the section of the cylinder, which as I have
said is a circle with the axis of rotation at the centre. He then
supp